On long-term mortality trends in the United States, 1850–1968

This study of United States life tables analyzes the process of mortality transition during 1850–1968. Special features of the study are (1) a phase-specific, rather than an age-specific, analysis of mortality and (2) use of measures based on person-years of life (nL _x ) in phase-intervals, rather than survival rates (nPx) or expectation of life at given ages (e _x ^o). The analysis suggests that the historical transition of mortality in the United States can be described as a three-stage process: an initial stage of slow improvement in life expectancy during 1850–1900, a second stage of rapid improvement during 1900–1950, and a third stage of slower improvement since 1950. Quantitative measures of rapidity of mortality decline in the several phases indicate that they are not identical for all phases and in all stages. The analysis also suggests that there have been rapid changes in the components of overall mortality differentials by sex and race in the United States. The paper draws attention to the need for studies of factors in variations of mortality at ages beyond 50 in the United States population subgroups.     

Relationship between surplus energy and body weight in fish populations

Summary This paper theoretically analyses the relationship between surplus energy, which is available for either somatic growth or reproduction, and body weight. From the data of metabolism and growth of the biwamasu,Oncorhynchus rhodurus, obtained by Miura et al., a Bernoulli's differential equation is induced to represent the relationship between body weight and the sum of surplus energy and active metabolic rate. Solving this equation gives the amount of surplus energy,f(W_x), as follows:f(W_x) = (αW _x ^1−γ +β^1−γ)^1/(1−γ)−W_x, in which α, β and γ are constants andW _x is body weight at agex. The function is applied to ten fish populations and consequently it is found to be useful for a wider age range and a wider variety of fishes than the conventional function.     

Counter-Examples about Lower- and Upper-Bounded Population Growth

ABSTRACT

For a unimodal growth function f having its maximum at a critical state x _c , the interval bounding the population size asymptotically is usually presented as being equal to [f ^○2(x _c ), f(x _c )]. This interval however does not represent the maximum range within which the population size can vary, even asymptotically. The actual invariant interval containing the population size is equal to: [min(x*, f ^○2(x _c )), f(x _c )], where x* denotes the non-zero fixed point, assumed to be unique, of the iteration of f.     

Inequality in Life Spans and a New Perspective on Mortality Convergence Across Industrialized Countries

The second half of the twentieth century witnessed substantial convergence in life expectancy around the world. We examine differences in the age pattern of mortality in industrialized countries over time to show that inequality in adult life spans, which we measure with the standard deviation of life table ages at death above age 10 years, S₁₀, is increasingly responsible for the remaining divergence in mortality. We report striking differences in level and trend of S₁₀ across industrialized countries since 1960, which cannot be explained by aggregate socioeconomic inequality or differential external‐cause mortality. Rather, S₁₀ reflects both within‐ and between‐group inequalities in life spans and conveys new information about their combined magnitudes and trends. These findings suggest that the challenge for health policies in this century is to reduce inequality, not just lengthen life.     

Measurement of non-randomness in spatial distributions

Summary The measurement of departure from randomness in spatial distributions has widespread application in ecological work. Several “indices of non-randomness” are compared with regard to their dependence on sample number, sample size and density. Criteria for the best choice of index for specific situations are discussed. A new coefficientC _x is proposed for use with positively contagious distributions and tests of significance are given. WhenC _x and another index (S ²/m−1) are used for positive and negative contagion respectively, values ranging from −1 through 0 (random) to +1 are obtained, regardless of sample number, sample size or density.     

Adult population parameters and life tables of an epilachnine beetle (Coleoptera: Coccinellidae) feeding on bitter cucumber in Sumatra

Summary The population dynamics of an epilachnine beetle, which is closely related toEpilachna sparsa Dieke (henceforth called “sp. C”) and feeds on bitter cucumberMomordica charantia, was studied by mark-recapture of adults and the construction of life tables. The study was repeated three times, i.e., March–May, July–September and October–December in 1982, in Padang, Sumatra, Indonesia. After the establishment of the host plants, adults of “sp. C” soon colonized, and each study period ended in the death of the plants due to defoliation by the larvae and adults. The estimated mean length of residence of adults ranged from 6–11 days, but this was probably much shorter than the actual longevity, because the adults were so active that they flew away, or dropped off the plants, when they were approached or slightly disturbed. Life tables indicated that egg mortality ranged from 17.8–53.9%, and a parasitic waspTetrastichus sp. B made up 41.1–64.2% of egg mortality. Two wasps,Tetrastichus sp. C andPediobius foveolatus killed 1.2–19.4% (7.6–100%)^* of 4th instars and only the latter species attacked the pupae, killing 24.6–59.1% (45.1–72.4%). Parasitism and starvation by overcrowding contributed most to the total mortality from egg to adult emergence, which ranged from 89.4–99.5%. “Sp. C” had a higher diversity and level of parasitism than the Japanese species,E. vigintioctopunctata. The high dispersal power of “sp. C”, coupled with the prolongedl _x−m_x schedules shown under laboratory conditions, was advantageous for exploiting the food plant which was available throughout the year, but was rather patchily distributed in space.     

Loss of genetic variability in a fragmented continuously distributed population

An individual-based simulation model was used to examine the effect of population subdivision, dispersal distance of offspring, and migration rates between subpopulations on genetic variability(H ₁ H _S andH _T ) in a continuously distributed population. Some difficulties with mathematical models of a continuously distributed population have been pointed out. The individual-based model can avoid these difficulties and can be used to examine genetic variability in a population within which individuals are distributed continuously and in which the dispersal of individuals is disturbed by geographical or artificial barriers. The present simulation showed that the pattern of decrease inH ₁ had three stages. During the first stage,H ₁ decreased at the rates predicted by Wright’s neighborhood size. During the second stage,H ₁ decreased more rapidly when the migration rate decreased, while during the third stage, it decreased less rapidly when the migration rate decreased. Increasing the number of subdivisions increased the rate of decrease after the 200th generation. The pattern of decrease inH _T was classified into 2 stages. During the first stage, the rates of decrease corresponded with those of a randomly mating population. During the second stage, a decrease in the migration rates of the subpopulations slowed the rate of decrease inH _T . A uniform spatial distribution and a reduced total dispersal distance of offspring causedH ₁ H _S , andH _T to decrease more rapidly. Habitat fragmentation in a continuously distributed population usually was detrimental to the genetic variability in the early generations. Other implications of the results for conservation are discussed.     

Calculating life tables by estimating Chiang’s a from observed rates

A simple, accurate method of life table construction is advanced based upon a new way to estimate Chiang’s _n a _x (the average number of years lived in the x to x + n age interval by those dying in the interval). The estimate for _n a _x leads immediately to an expression for l _x+n (the survivors to age x + n) in terms of l _x and the known mortality rates for the interval x to x+n and the two adjacent intervals. The complete solution for the basic life table is given. The proposed method and five other easily applied methods are then compared against the standard provided by the U.S. life tables for 1969–1971. The results attest to the excellent performance and high degree of accuracy of the proposed method. Finally, extensions of the method to multiple decrement and associated single decrement life tables are briefly described.     

Dynamics of Mixed Coalitions Under Social Cohesion Constraints

ABSTRACT

Parameters for the birth and death diffusion life table model subject to downward jumps randomly occurring at a constant rate are estimated. The jump magnitudes have a beta distribution with support [0, l_x ], where l_x is the total number of survivors prior to the jump. The estimation method is maximum likelihood. The Cramer–Rao Lower bound and the asymptotic distribution for the MLE are derived. The model is applied to the U.S. men′s population from 1900 to 1999.     

Life tables for worker honeybees

Summary Life tables for worker honeybees covering all life span, and those for adults, were prepared for three seasonal cohorts,June bees, July bees andwintering bees. Survivorship curves forJune andJuly bees show a convex type being exceptional for insects, with relatively high mortality at egg and feeding larval stages and at later adult stage after most bees became potential foragers. Adult longevity greatly lengthens inWinteriing bees and survivorship curve drops approximately with the same rate. A remarkable similarity of survivorship curves for men and honeybees was demonstrated, apparently due to highly developed social care in both. Some comments were given on mortality factors. The importance of life tables for population researches was shown by applying our result to the population growth curve made byBodenheimer, based upon the data byNolan. At the asymptote of the uncorrected curve, the ratio of total population estimated by uncorrected curve to that by corrected curve reaches about 3∶2. Contribution No. 821 from the Zoological Institute, Faculty of Science, Hokkaido University, Sapporo, Japan. Contributions from JIBP-PT No. 45. This study was in part supportod by a grant in aid from the Ministry of Education for the special project research, “Studies on the dynamic status of biosphere.” Population and bioeconomic studies on the honeybee colonies. II. We express our sincere thanks to Dr. YosiakiIt?, National Institute of Agricultural Sciences, Tokyo, for his kind stimulation and advices to the present work.     

Spatial pattern indices based on distances between individuals on a line-segment with finite length

Summary Let us consider a strip-wise habitat of line-segment, like a corridor, to simplify the subject mathematically, and assume that the length of the habitat is γ and there aren individuals. Here, we assume that the spatial pattern of the individuals is random if then distances from the left end of the habitat to each individual follow a uniform distribution on the strip. Under such an assumption, the variance of the distances between any two neighbors is represented by the formulanθ ²(n+1)⁻²(n+2)⁻¹ and the variance betweenn+1 distances betweenn individuals from the left end to the right end to the strip, is represented by the formulanθ ²(n+1)⁻²(n+2)⁻¹. These two kinds of variances can be used for determining (1) the spatial pattern of a population on the strip and (2) the spatial structure within the population, by comparison with the variances calculated from the data. Two examples cited from the literature, a cattle population on a pasture and an aphid population on a sycamore leaf, are presented.     

A probabilistic interpretation of the United Nations’ 1995–2005 population projections

I develop probabilistic interpretations for the United Nations’ 10-year population forecasts by comparing 1995 projections for 212 countries to the population sizes reported for 2005. Errors in the estimation of the intrinsic rate of increase, presumably caused by erroneous assumptions about birth, death and/or immigration rates, appear to be more consequential than errors based on inaccurate estimation of the starting, or ‘jump-off’, population size. For only about 20% of the countries did the ‘actual’ 2005 population size fall between the United Nations’ low- and high-variant projections. I propose prediction intervals for country-specific population sizes 10 years in the future of the form [ N_i^￠ (t+10) / k ,  k ·N_i^￠ (t+10) ],[ N_i^{\prime} (t+10) / k , \, k \cdot N_i^{\prime} (t+10) ], where N _i ′(t + 10) is the medium-variant prediction for year t + 10 made in year t, and k is a number that varies with starting population size. Based on the 1995–2005 United Nations’ data, values of k giving 95% coverage range from 1.11 for countries with a population on the order of 10⁹, to 1.45 for countries with a population of 10⁵.     

Biology ofHyphantria cuneaDrury (Lepidoptera: arctiidae) in Japan. V. Preliminary life tables and mortality data in urban areas

Summary Studies on the population dynamics of the fall webworm,Hyphantria cunea have been carried out at three survey stations and along selected roads in the urban area of Tokyo since 1966. Twelve survivorship curves obtained during two years and 8 life tables show that the mortality rate in early developmental stages of the fall webworm is remarkably low as compared with that of other lepidopterous defoliaters and the mortality rate in later developmental stages is compensatory high. The low mortality rate in early stages is considered to be due to the protective role of the nest-web and the lack of egg and larval parasites. All but one parasitic species emerge from prepupae and pupae. Spiders living in the nest-web of the fall webworm play an important role in reducing the number of young larvae. Direct observations and caging experiments showed that relatively high mortality during later larval stages is mainly due to predation by birds (in the first generation) and wasps (in the second generation). The generation mortality in the survey stations always exceeded the level where the population is kept at the steady state, and the outbreak of this moth is considered to be continued by the immigration of adults from large trees growing in gardens on which the larvae can escape from predation pressure. Contributions from JIBP-PT No. 51. A part of this study was supported by the special project research, ‘Studies on the dynamic status of biosphere’, sponsored by the Ministry of Education.     

The momentum of mortality change

Mortality change is not usually assigned much importance as a source of population growth when future population trends are discussed. Yet it can make a significant contribution to population momentum. In populations that have experienced mortality change, cohort survivorship will continue varying for some time even if period mortality rates become constant. This continuing change in cohort survivorship can create a significant degree of mortality-induced population change, a process we call the ‘momentum of mortality change’. The momentum of mortality change can be estimated by taking the ratio of e ₀ (the period life expectancy at birth) to CAL (the cross-sectional average length of life) for a given year. In industrialized nations, the momentum of mortality change can attenuate the negative effect on population growth of declining fertility or sustained below-replacement fertility. In India, where population momentum has a value of 1.436, the momentum of mortality change is the greatest contributor to its value.     

Black–White Disparities in Adult Mortality: Implications of Differential Record Linkage for Understanding the Mortality Crossover

Mortality rates among black individuals exceed those of white individuals throughout much of the life course. The black–white disparity in mortality rates is widest in young adulthood, and then rates converge with increasing age until a crossover occurs at about age 85 years, after which black older adults exhibit a lower mortality rate relative to white older adults. Data quality issues in survey-linked mortality studies may hinder accurate estimation of this disparity and may even be responsible for the observed black–white mortality crossover, especially if the linkage of surveys to death records during mortality follow-up is less accurate for black older adults. This study assesses black–white differences in the linkage of the 1986–2009 National Health Interview Survey to the National Death Index through 2011 and the implications of racial/ethnic differences in record linkage for mortality disparity estimates. Match class and match score (i.e., indicators of linkage quality) differ by race/ethnicity, with black adults exhibiting less certain matches than white adults in all age groups. The magnitude of the black–white mortality disparity varies with alternative linkage scenarios, but convergence and crossover continue to be observed in each case. Beyond black–white differences in linkage quality, this study also identifies declines over time in linkage quality and even eligibility for linkage among all adults. Although linkage quality is lower among black adults than white adults, differential record linkage does not account for the black–white mortality crossover.     

Evaluation of statistical precision and design of efficient sampling for the population estimation based on frequency of occurrence

Summary The binomial sampling to estimate population density of an organism based simply upon the frequency of its occurrence among sampled quadrats is a labour-saving technique which is potentially useful for small animals like insects and has actually been applied occasionally to studies of their populations. The present study provides a theoretical basis for this convenient technique, which makes it statistically reliable and tolerable for consistent use in intensive as well as preliminary population censuses. Firs, the magnitude of sampling error in relation to sample size is formulated mathematically for the estimate to be obtained by this indirect method of census, using either of the two popular models relating frequency of occurrence (p) to mean density (m), i.e. the negative binomial model,p=1−(1+m/k) ^−k, and the empirical model,p=1−exp(−am ^b). Then, the equations to calculate sample size and census cost that are necessary to attain a given desired level of precision in the estimation are derived for both models. A notable feature of the relationship of necessary sample size (or census cost) to mean density in the frequency method, in constrast to that in the ordinary census, is that it shows a concave curve which tends to rise sharply not only towards lower but also towards higher levels of density. These theoretical results make it also possible to design sequential estimation procedures based on this convenient census technique, which may enable us with the least necessary cost to get a series of population estimates with the desired precision level. Examples are presented to explain how to apply these programs to acutal censuses in the field.     

The dynamics of laboratory populations ofCallosobruchus chinensis andC. Maculatus (Coleoptera: Bruchidae) in patchy environments

Summary Experiments are described showing the long-term dynamics of two species of bruchid beetles (Callosobruchus chinensis andC. maculatus) in arenas in which the resource of 50 black-eyed beans is divided between 5, 10 or 50 ‘patches’. Both species of adult beetles exhibit clumped distributions between patches. Within a patch there is a tendency for a density dependent reduction in (1) eggs laid per female, (2) the proportion of eggs hatching per bean (C. chinensis only) and (3) larval survival which is strongly overcompensating (particularly inC. maculatus). A discrete generation model is used as a framework to draw these results together and show how the different factors affecting natality and mortality can influence the population dynamics. Finally, the importance of the resource renewal interval in influencing the period of the population cycles is discussed.     

Yearly variation in recruitment and its effect on population dynamics inYoldia notabilis (Mollusca: Bivalvia), analyzed using projection matrix model

Summary Long-term variation in recruitment was estimated by constructing projection matrices for a marine bivalve,Yoldia notabilis, at two stations in Otsuchi Bay, northeastern Japan, and the effects of its variation on population dynamics were examined using a simple matrix model. The matrix model was developed from the Leslie matrix, in which the population growth rate λ was expressed as a function of recruitment rater ₀. The equilibrium recruitment rater _s, or the recruitment rate required to maintain population at constant size (λ=1), was expressed by the reciprocal of the reproductive value of a newly recruited individual. The estimates ofr _s for the field population were lower at the shallower station than at the deeper station, reflecting higher survivorship and fecundity. Past recruitment rate estimated both by the field samplings for 3 years and by the back-calculation from the current age structure for over 10 years showed large yearly variation, ranging between 0 and 58.6×10⁻⁴. The estimates were larger thanr _s, and hence, large enough to increase population size (λ>1) only in approximately one-third of the estimated years. This suggests that the population has been maintained by occasional successful recruitment occurring once every few years.     

Settling-site selection and survival of two scale insects,Ceroplastes rubens andC. ceriferus, on citrus trees

Summary We studied settling-site selection and the resulting survival of two sessile scale insects,Ceroplastes rubens andC. ceriferus, in the citrus tree,Citrus unshiu, in central Japan. C. rubens preferred 0-year-old twigs most as a settling-site; the density of nymphs settling on 0-year-old twigs was significantly higher than those on ≥1-year-old twigs, and few nymphs settled on ≥3-year-old twigs. The mean survival rates from settling until reproduction in the next year were significantly higher on more preferred twigs than on less preferred ones. InC. ceriferus, nymphs significantly preferred 1- and 2-year-old twigs to 0- and ≥3-year-old ones, and the mean survival rates on the more preferred 1- and 2-year-old twigs were significantly higher than those on less preferred ≥3-year-old twigs. However, the survival rate on less preferred 0-year-old twigs was slightly higher than those on 1- and 2-year-old ones. Thus, in both species of scale, it was the preferred twigs which were more profitable sites for survival after settling, except for less preferred 0-year-old twigs forC. ceriferus. In both scale species, most mortality was due to growth cessation, which is believed to be related to the twig quality as a food source. Predators and parasitoids were minor mortality factors. Both species showed constant survival rates until the density of settled nymphs exceeded double the “upper-limit” density, whereupon they decreased drastically. Nymphs ofC. rubens settling on twigs of high scale density showed a spacing-out distribution, those ofC. ceriferus did not. InC. rubens, an increase in preference for originally less profitable twigs at the later stage of the settling season was observed, but not inC. ceriferus. Accordingly, individuals ofC. rubens showed a stronger tendency to avoid conspecifics than didC. ceriferus. Although nymphs of the two scales clearly preferred more profitable sites, their settling-site selection did not agree with the predictions from the ideal free distribution theory (Fretwell and Lucas, 1970). The discrepancies were (1) frequent settling on less profitable sites at the early stage of the settling season, (2) insufficient utilization of the most profitable twigs, and (3) virtually 100% mortality on overcrowded twigs under conditions where unoccupied profitable twigs still remained. These discrepancies are thought due to the limited dispersal time of nymphs. Contribution to the ecological studies of scale insects 2.     

Losses of Expected Lifetime in the United States and Other Developed Countries: Methods and Empirical Analyses

Patterns of diversity in age at death are examined using e ^†, a dispersion measure that equals the average expected lifetime lost at death. We apply two methods for decomposing differences in e ^†. The first method estimates the contributions of average levels of mortality and mortality age structures. The second (and newly developed) method returns components produced by differences between age- and cause-specific mortality rates. The United States is close to England and Wales in mean life expectancy but has higher life expectancy losses and lacks mortality compression. The difference is determined by mortality age structures, whereas the role of mortality levels is minor. This is related to excess mortality at ages under 65 from various causes in the United States. Regression on 17 country-series suggests that e ^† correlates with income inequality across countries but not across time. This result can be attributed to dissimilarity between the age- and cause-of-death structures of temporal mortality reduction and intercountry mortality variation. It also suggests that factors affecting overall mortality decrease differ from those responsible for excess lifetime losses in the United States compared with other countries. The latter can be related to weaknesses of health system and other factors resulting in premature death from heart diseases, amenable causes, accidents and violence.